Abstract: In this work the effects of sharp edges in the electronic properties of graphene lattices in the quantum Hall regime were studied. The problem was addressed using the tight-binding approximation including the effects of the magnetic eld and disorder in the
model. It was studied at rst the effect of the edges in the energy levels of the system,
through Hofstadter's buttery-like spectrum. Then we focused on analysing the localization
properties of edge states and the particularities of the wave function distributions for
these cases. To investigate the edge states and to determine, for each electronic state, how
much of the wave function is localized at the edges, it was created a quantity called Edge
Fraction. This quantity was dened as the probability density sum in the edge region,
which in a semi-classical approximation, was considered here as the region limited by a
distance 2'B from the edges, where 'B is the magnetic length. Using the Edge Fraction and analysing the contributions of armchair and zigzag edges separately, in squared lattices, it was found that there are energy regions where the wave functions are clearly more localized in a specic edge type. This behaviour is believed to be a result of the competition between the potential due to the presence of the edge and the potential due to the disorder in the system, which are also present in the Hofstadter energy spectrum. The results obtained contribute to the understanding of the localization properties of graphene lattices with edges